A person starts from a point A and travels 3 km eastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. The shortest distance between the starting point and destination is

To solve this problem, we can track the movement of the person on a coordinate plane starting from point A at 0, 0.

Step 1: The person travels 3 km east to point B. The coordinates of B are 3, 0.

Step 2: He turns left north and travels thrice that distance 3 times 3 equals 9 km to reach C. The coordinates of C are 3, 9.

Step 3: He turns left west and travels five times the original distance 5 times 3 equals 15 km to reach D. Since he starts this leg at x coordinate 3 and moves 15 units west, his final x coordinate is 3 minus 15 which equals negative 12. The coordinates of D are negative 12, 9.

Step 4: The shortest distance between point A 0, 0 and point D negative 12, 9 is calculated using the Pythagorean theorem.

Distance equals the square root of the sum of the squares of the horizontal and vertical displacements. Horizontal displacement is 12 km. Vertical displacement is 9 km. Distance equals square root of 12 squared plus 9 squared. Distance equals square root of 144 plus 81. Distance equals square root of 225. Distance equals 15 km.

Therefore, the shortest distance is 15 km. Correct option is C.